Voltammetry: diffusion written in current

People with diabetes prick their fingers several times a day. On the test strip an enzyme oxidises the glucose in the blood and hands the electrons to a “mediator” (often potassium ferricyanide); the meter applies a potential that reoxidises the reduced mediator and reads the current over a few seconds — a current proportional to the glucose concentration. Potentiometry measures a voltage while no current flows; voltammetry does the opposite: it controls the potential and measures the current. That current records how fast the reactant diffuses to the electrode, and how fast electrons cross.

A voltammetric cell has three electrodes. The reaction happens at a small working electrode (a glassy-carbon, platinum or gold disc); the reference electrode only measures and controls the working electrode’s potential and carries almost no current; the current returns through the counter electrode (a platinum wire). A potentiostat keeps adjusting the voltage on the counter electrode so that the working electrode sits at the set potential against the reference.

At the surface the ratio of oxidised form O to reduced form R obeys the Nernst equation — change the potential and the surface concentrations change at once. But reactant from the bulk has to reach the surface, by diffusion (driven by concentration gradients), migration (ions pushed by the field) or convection (stirring or thermal currents). A supporting electrolyte such as 0.1–1 M KCl carries the current so that migration of the analyte is negligible; with the solution still, only diffusion remains.

Step the potential suddenly to a value that oxidises every R at the surface: the surface concentration drops to zero and a depleted layer starts growing into the solution, about $\sqrt{\pi Dt}$ thick — some 47 µm after 1 s and 150 µm after 10 s. The current is proportional to the concentration gradient at the surface, which flattens as the layer thickens, so the current decays as $1/\sqrt{t}$ — the Cottrell equation, the basis of chronoamperometry and of many electrochemical sensors.

Cyclic voltammetry sweeps the potential linearly at a rate v to a switching potential and back. Starting well below E°′ and sweeping positive, R at the surface begins to oxidise and the current rises; past E°′ the surface is nearly depleted, the current becomes diffusion-limited and falls as the depleted layer thickens — hence a peak. On the return sweep the O piled up near the electrode is reduced again, giving a peak of opposite sign.

For a reversible (Nernstian) couple with fast electron transfer:

• the mean of the two peak potentials ≈ the formal potential $E^{\circ\prime}$;
• the peak separation $\Delta E_\mathrm{p} = E_\mathrm{pa} - E_\mathrm{pc} \approx 59/n$ mV at 25 °C (57–60 mV depending on the switching potential) and does not change with v;
• the peak current $i_\mathrm{p}$ is proportional to $\sqrt{v}$ and to concentration, and $i_\mathrm{pa}/i_\mathrm{pc} \approx 1$.

When electron transfer is slower (quasi-reversible), the surface cannot keep up with Nernstian equilibrium, extra overpotential is needed, and the peaks move apart — further apart the faster the scan. Nicholson described this with the parameter $\psi = k^\circ/\sqrt{\pi D n F v/RT}$.